Geodesic
Noncommutative Classical and Quantum Mechanics for Quadratic Lagrangians (Hamiltonians)
Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 90-100

Voir la notice de l'article provenant de la source Math-Net.Ru

Classical and quantum mechanics based on an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates are considered. In this approach additional noncommutativity is removed from the algebra by a linear transformation of coordinates and transferred to the Hamiltonian (Lagrangian). This linear transformation does not change the quadratic form of the Hamiltonian (Lagrangian), and Feynman's path integral preserves its exact expression for quadratic models. The compact general formalism presented here can be easily illustrated in any particular quadratic case. As an important result of phenomenological interest, we give the path integral for a charged particle in the noncommutative plane with a perpendicular magnetic field. We also present an effective Planck constant $\hbar _\mathrm{eff}$ which depends on additional noncommutativity. 
@article{TRSPY_2009_265_a6,
     author = {B. Dragovich and Z. Raki\'c},
     title = {Noncommutative {Classical} and {Quantum} {Mechanics} for {Quadratic} {Lagrangians} {(Hamiltonians)}},
     journal = {Informatics and Automation},
     pages = {90--100},
     publisher = {mathdoc},
     volume = {265},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a6/}
}
TY  - JOUR
AU  - B. Dragovich
AU  - Z. Rakić
TI  - Noncommutative Classical and Quantum Mechanics for Quadratic Lagrangians (Hamiltonians)
JO  - Informatics and Automation
PY  - 2009
SP  - 90
EP  - 100
VL  - 265
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a6/
LA  - en
ID  - TRSPY_2009_265_a6
ER  - 
%0 Journal Article
%A B. Dragovich
%A Z. Rakić
%T Noncommutative Classical and Quantum Mechanics for Quadratic Lagrangians (Hamiltonians)
%J Informatics and Automation
%D 2009
%P 90-100
%V 265
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a6/
%G en
%F TRSPY_2009_265_a6
B. Dragovich; Z. Rakić. Noncommutative Classical and Quantum Mechanics for Quadratic Lagrangians (Hamiltonians). Informatics and Automation, Selected topics of mathematical physics and $p$-adic analysis, Tome 265 (2009), pp. 90-100. http://geodesic.mathdoc.fr/item/TRSPY_2009_265_a6/